Polyphemus pediculus (L.) is a small (1 mm long) predatory crustacean that lives in bodies of standing freshwater. It has a single fused compound eye, which occupies most of its head. The eye comprises 130 ommatidia with five distinct types of crystalline cones. Four of these cone types were found to focus light by means of gradient index optics (lens cylinders). The edge ommatidia differ by having the focus displaced below the distal rhabdom tip. This was found to be correlated with their special type of rhabdom, which is characterized by its short, broad shape and the absence of a palisade. The central-type crystalline cone, contributing to a zone of acute vision, is functionally different from the other four cone types. The focusing on the rhabdom tip is in this case achieved by a prism, inside the cone, corrected for optical aberration with a complex refractive index gradient. The prism is interpreted as a way of compressing a long focal length into a short optical system, i.e. to enable high resolution in spite of the small size of the eye. Extreme regional differences in interommatidial angles were found to be the main reason for the different optical design between central and peripheral ommatidia.